# What are AC Bridges & General form of AC Bridges

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## What are AC Bridges?

#### In an ac bridge, each of the four arms is an impedance, and the battery and the galvanometer of the Wheatstone bridge are replaced respectively by an ac source and a detector sensitive to small alternating potential differences.

The usefulness of ac bridge circuits is not restricted to the measurement of unknown impedances and associated parameters like inductance, capacitance, storage factor, dissipation factor etc.

#### For measurements at low frequencies, the power line may act as the source of supply to the bridge circuits.For higher frequencies, electronic oscillators are universally used as bridge source supplies. These oscillators have the advantage that the frequency is constant, easily adjustable, and determinable with accuracy.

The waveform is very close to a sine wave, and their power output is sufficient for most bridge measurements.A typical oscillator has a frequency range of 40 Hz to 125 kHz with a power output of 7 W.

### General Equation for AC Bridge Balance:

#### The below figure shows a basic ac bridge.The four arms of the bridge are impedances Z1,Z2,Z3 & Z4. #### The conditions for the balance of bridge require that there should be no current through the detector.This requires that the potential difference between points b and d should be zero.This will be the case when the voltage drop from a to b equals to voltage drop from a to d, both in magnitude and phase.In complex notation we can, thus, write : #### Above two equations represent the basic equations for the balance of an ac bridge.Equation Z1 Z4 = Z2 Z3  is convenient to use when dealing with series elements of a bridge while Equation Y1 Y4 = Y2 Y3 is useful when dealing with parallel elements.

Equation Z1 Z4 = Z2 Z3 states that the product of impedances of one pair opposite arms must equal the product of impedances of the other pair of opposite arms expressed in complex notation.This means that both magnitudes and the phase angles of the impedances must be taken into account.

#### If we work in terms of rectangular coordinates, we have

Z1= R1 + jX1 ;                       Z2= R2 + jX2
Z3= R3 + jX3            and         Z4= R4 + jX4
For balance,             Z1 Z4 = Z2 Z3
or     (R1 + jX1)(R4 + jX4) = (R2 + jX2)(R3 + jX3)
or    R1 R4 – X1 X4 + j(X1R4 + X4R1) = R2 R3 – X1 X4 + j(X2R3 + X3R2)

The above equation is a complex equation and a complex equation is satisfied only if real and imaginary parts of each side of the equation are separately equal. Thus, for balance,

R1 R4 – X1 X4 = R2 R3 – X1 X4
X1R4 + X4R1 = X2R3 + X3R2
Thus there are two independent conditions for balance and both of them must be satisfied for the ac bridge to be balanced.

### General Form of AC Bridges:

#### Equating the real and imaginary parts separately, we have, #### (adsbygoogle = window.adsbygoogle || []).push({}); The technique of balancing is to adjust L2 till a minimum indication is obtained on the detector, then to adjust R2 until a new smaller minimum indication is obtained.Then L2 and R2 are alternately adjusted until the detector shows no indication. #### The process of alternate manipulation of two variable elements is rather typical of the general balancing procedures adopted in most ac bridges. When two variables are chosen such that the two balance equations are no longer independent, the ac bridge has a very poor convergence of balance and gives the effect of sliding balance.

The term Sliding Balance describes a condition of interaction between the two controls. Thus when we balance with R2, then go to R3 and back to R2 for adjustment, we find a new apparent balance.

#### Thus the balance point appears to move, or slide and settles only gradually to its final point after many adjustments.It may be emphasised here that in case the two balance conditions are independent, not more thane two or three adjustments of the variable elements would be necessary to obtain balance.

In case we choose the two variable components such that the two equations are not independent the balance procedure becomes laborious and time-consuming.

#### For example, if we choose R2 and R3 as variable elements, the two equations are no longer independent since R3 appears in both the equations. There are two adjustments, one resistive and the other reactive that must be made to secure balance.

For the usual magnitude responsive detector, these adjustments must be made alternately until they converge on the balance point. The convergence to balance point is best when both the variable elements are in the same arms.

#### 4.In this bridge circuit, balance equations are independent of frequency. This is often a considerable advantage in an ac bridge, for the exact value of the source frequency, need not then be known.Also, if a bridge is balanced for a fundamental frequency it should also be balanced for any harmonic and the wave-form of the source need not be perfectly sinusoidal.

On the other hand, it must be realized that the effective inductance and resistance for example, of a coil, vary with frequency, so that a bridge balanced at a fundamental frequency is never, in practice, truly balanced for the harmonics.

#### To minimize difficulties due to this the source waveform should be good, and it is often an advantage to use a detector tuned to the fundamental frequency.Further, while the disappearance of the frequency factor is of advantage in many ac bridges, some bridges derive their usefulness from the presence of a frequency factor.

Such bridges must then be supplied from a source with very good wave-form and high frequency stability.Alternatively, they may be used to determine frequency.

READ HERE  Measurement of Self Inductance by Owen's Bridge